--- Math utilities.
-- @module advtrains_doc_integration.mathutils
-- @alias M
local M = {}

local function gcdmain(x, y, ...)
	if y == nil then
		return x or 1
	end
	y = y%x
	if y == 0 then
		return gcdmain(x, ...)
	end
	return gcdmain(y, x, ...)
end

--- Compute the greatest common divider.
-- @tparam integer ... The numbers used for the computation.
-- @treturn integer The GCD of the given numbers.
function M.gcd(...)
	local args = {...}
	for k, v in pairs(args) do
		if v == 0 then
			return 0
		elseif v ~= v then
			return v
		elseif v < 0 then
			args[k] = -v
		end
	end
	return gcdmain(unpack(args))
end

--- Reduce a fraction.
-- @tparam integer num The numerator.
-- @tparam integer denom The denominator.
-- @treturn int,int The reduced fraction.
function M.reduce_fraction(num, denom)
	local gcd = M.gcd(num, denom)
	return num/gcd, denom/gcd
end

return M